Using linear-quadratic control theory

a stochastic differential game problem between investor and market with liability is investigated

in which the liability process is assumed to be a geometric Brownian motion and completely correlated with stock prices

with the market as the hypothetical counterpart and the investor as the leader of game. Under exponential utility and power utility

optimal investment strategies and optimal market strategies as well as the closed form expression of the value function are obtained. Though further analyzing of the results

some explanations in economic are given.